I assume measuring the depth of the dovetail is not an issue.
The classic manual technique is what jko describes, using two pairs of gage pins (or just one pair if the angle is known to be good a-priori). When doing this, you should also account for any difference in depth on the two sides, by the way.
If the CMM machine has some kind of spherical probe you ...
You could take an over or between pins measurements if it's the male or female part. Take 2 measurements using 2 different diameter pair of pins. Assuming the edges are fairly straight you should be able to deduce the dovetail angle.